To determine the maximum height attained by the stone and the time taken to achieve this height, we can use the equations of motion.
Let's assume the initial velocity of the stone when thrown upward is u = 98 m/s (positive because it is directed upward), the final velocity at the highest point is v = 0 m/s, and the acceleration due to gravity is a = -9.8 m/s² (negative because it acts downward).
We can use the following equation to find the time taken to reach the maximum height (time of flight):
v = u + at
0 = 98 - 9.8t
Solving this equation for t:
9.8t = 98
t = 98 / 9.8
t ≈ 10 seconds
The time taken to reach the maximum height is approximately 10 seconds.
To find the maximum height (h), we can use the equation:
h = ut + (1/2)at²
h = 98(10) + (1/2)(-9.8)(10)²
h = 980 - 490
h = 490 meters
Therefore, the maximum height attained by the stone is 490 meters.